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Issue 1

Combinatorial rule explosion eliminated by a fuzzy rule configuration
W. E. Combs, J. E. Andrews
Boeing Co., Seattle, WA, USA
vol. 6, no. 1, pp. 1-11, Feb. 1998

Conventional fuzzy inference methodology relates the relevant subsets of each input universal set to the subsets of the other system inputs through an intersection-rule configuration. This strategy yields an exponential growth in the number of rules as inputs are added to the system, quickly reducing performance to unacceptable levels. A novel rule configuration and matrix design are presented in this paper that do not rely on rule multiplication to insure that antecedent elements are effectively related to their consequent counterparts. This alternative formulation models the entire system problem space with a simplified structure that increases linearly as the inference engine grows, providing significant computational savings to a broad range of commercial and scientific applications.

An online self-constructing neural fuzzy inference network and its applications
Feng Juang Chia, Teng Lin Chin
Dept. of Control Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan
vol. 6, no. 1, pp. 12-32, Feb. 1998

A self-constructing neural fuzzy inference network (SONFIN) with online learning ability is proposed in this paper. The SONFIN is inherently a modified Takagi-Sugeno-Kang (TSK)-type fuzzy rule-based model possessing neural network learning ability. There are no rules initially in the SONFIN. They are created and adapted as online learning proceeds via simultaneous structure and parameter identification. In the structure identification of the precondition part, the input space is partitioned in a flexible way according to an aligned clustering-based algorithm. As to the structure identification of the consequent part, only a singleton value selected by a clustering method is assigned to each rule initially. Afterwards, some additional significant terms selected via a projection-based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds. The combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network, a main feature of the SONFIN. In the parameter identification, the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm. To enhance the knowledge representation ability of the SONFIN, a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved.

Entropy-based operations on fuzzy sets
I. J. Rudas, M. O. Kaynak
Dept. of Inf. Technol., Banki Donat Polytech., Budapest, Hungary
vol. 6, no. 1, pp. 33-40, Feb. 1998

By using a fuzzy entropy approach, three sets of new generalized operators are presented. After a general discussion on fuzzy entropy, the concept of an elementary entropy function of a fuzzy set is introduced. Using this mapping, the generalized intersections and unions are defined as mappings that assign the least and the most fuzzy membership grade to each of the elements of the domain of the operators, respectively. It is shown that these operators can be constructed from the conventional min and max operations. Next, two modified sets of operations are introduced. The second part of the paper investigates the applicability of the new operators in fuzzy logic controllers. Simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers. It is concluded that the first set of operators does not provide stable control, but the performance of the fuzzy controller can be improved by using the modified operations for a class of plants.

Analysis and design of fuzzy controller and fuzzy observer
Jun Ma Xiao, Qi Sun Zeng, Yan He Yan
Dept. of Comput. Sci. & Technol., Tsinghua Univ., Beijing, China
vol. 6, no. 1, pp. 41-51, Feb. 1998

This paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of the separation property; that is, the fuzzy controller and the fuzzy observer can be independently designed. A numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer.

A geometric approach to edge detection
J. C. Bezdek, R. Chandrasekhar, Y. Attikouzel
Dept. of Comput. Sci., Univ. of West Florida, Pensacola, FL, USA
vol. 6, no. 1, pp. 52-75, Feb. 1998

This paper describes edge detection as a composition of four steps: conditioning, feature extraction, blending, and scaling. We examine the role of geometry in determining good features for edge detection and in setting parameters for functions to blend the features. We find that: (1) statistical features such as the range and standard deviation of window intensities can be as effective as more traditional features such as estimates of digital gradients; (2) blending functions that are roughly concave near the origin of feature space ran provide visually better edge images than traditional choices such as the city-block and Euclidean norms; (3) geometric considerations ran be used to specify the parameters of generalized logistic functions and Takagi-Sugeno input-output systems that yield a rich variety of edge images; and (4) understanding the geometry of the feature extraction and blending functions is the key to using models based on computational learning algorithms such as neural networks and fuzzy systems for edge detection. Edge images derived from a digitized mammogram are given to illustrate various facets of our approach.

Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks
C. W. Omlin, K. K. Thornber, C. L. Giles
Adaptive Comput. Technol., Troy, NY, USA
vol. 6, no. 1, pp. 76-89, Feb. 1998

There has been an increased interest in combining fuzzy systems with neural networks because fuzzy neural systems merge the advantages of both paradigms. On the one hand, parameters in fuzzy systems have clear physical meanings and rule-based and linguistic information can be incorporated into adaptive fuzzy systems in a systematic way. On the other hand, there exist powerful algorithms for training various neural network models. However, most of the proposed combined architectures are only able to process static input-output relationships; they are not able to process temporal input sequences of arbitrary length. Fuzzy finite-state automats (FFAs) can model dynamical processes whose current state depends on the current input and previous states. Unlike in the case of deterministic finite-state automats (DFAs), FFAs are not in one particular state, rather each state is occupied to some degree defined by a membership function. Based on previous work on encoding DFAs in discrete-time second-order recurrent neural networks, we propose an algorithm that constructs an augmented recurrent neural network that encodes a FFA and recognizes a given fuzzy regular language with arbitrary accuracy. We then empirically verify the encoding methodology by correct string recognition of randomly generated FFAs. In particular, we examine how the networks' performance varies as a function of synaptic weight strengths.

A method of identifying influential data in fuzzy clustering
H. Imai, A. Tanaka, M. Miyakoshi
Div. of Syst. & Inf. Eng., Hokkaido Univ., Sapporo, Japan
vol. 6, no. 1, pp. 90-101, Feb. 1998

In multivariate statistical methods, it is important to identify influential observations for a reasonable interpretation of the data structure. In this paper, we propose a method for identifying influential data in the fuzzy C-means (FCM) algorithm. To investigate such data, we consider a perturbation of the data points and evaluate the effect of a perturbation. As a perturbation, we consider two cases: one is the case in which the direction of a perturbation is specified and the other is the case in which the direction of a perturbation is not specified. By computing the change in the clustering result of FCM when given data points are slightly perturbed, we can look for data points that greatly affect the result. Also, we confirm an efficacy of the proposed method by numerical examples.

Adaptive fuzzy command acquisition with reinforcement learning
Teng Lin Chin, Chih Kan Ming
Dept. of Electr. & Control Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan
vol. 6, no. 1, pp. 102-21, Feb. 1998

Proposes a four-layered adaptive fuzzy command acquisition network (AFCAN) for adaptively acquiring fuzzy command via interactions with the user or environment. It can catch the intended information from a sentence (command) given in natural language with fuzzy predicates. The intended information includes a meaningful semantic action and the fuzzy linguistic information of that action. The proposed AFCAN has three important features. First, we can make no restrictions whatever on the fuzzy command input, which is used to specify the desired information, and the network requires no acoustic, prosodic, grammar, and syntactic structure, Second, the linguistic information of an action is learned adaptively and it is represented by fuzzy numbers based on alpha -level sets. Third, the network can learn during the course of performing the task. The AFCAN can perform off-line as well as online learning. For the off-line learning, the mutual-information (MI) supervised learning scheme and the fuzzy backpropagation (FBP) learning scheme are employed when the training data are available in advance. The former learning scheme is used to learn meaningful semantic actions and the latter learn linguistic information. The AFCAN can also perform online learning interactively when it is in use for fuzzy command acquisition. For the online learning, the MI-reinforcement learning scheme and the fuzzy reinforcement learning scheme are developed for the online learning of meaningful actions and linguistic information, respectively. An experimental system is constructed to illustrate the performance and applicability of the proposed AFCAN.

Stable and optimal fuzzy control of linear systems
Xin Wang Li
Dept. of Electr. & Electron. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong
vol. 6, no. 1, pp. 137-43, Feb. 1998

A number of stable and optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to a ball-and-beam system.

Application of a fuzzy classification technique in computer grading of fish products
B. G. Hu, R. G. Gosine, L. X. Cao, C. W. de Silva
Centre for Cold Ocean Resources Eng., Memorial Univ. of Newfoundland, St. John's, Nfld., Canada
vol. 6, no. 1, pp. 144-52, Feb. 1998

This work presents the enhancement and application of a fuzzy classification technique for automated grading of fish products. Common features inherent in grading-type data and their specific requirements in processing for classification are identified. A fuzzy classifier with a four-level hierarchy is developed based on the "generalized K-nearest neighbor rules". Both conventional and fuzzy classifiers are examined using a realistic set of herring roe data (collected from the fish processing industry) to compare the classification performance in terms of accuracy and computational cost. The classification results show that the generalized fuzzy classifier provides the best accuracy at 89%. The grading system can be tuned through two parameters-the threshold of fuzziness and the cost weighting of error types-to achieve higher classification accuracy. An optimization scheme is also incorporated into the system for automatic determination of these parameter values with respect to a specific optimization function that is based on process renditions, including the product price and labor cost. Since the primary common features are accommodated in the classification algorithm, the method presented here provides a general capability for both grading and sorting-type problems in food processing.

A fuzzy logic-based predictor for predictive coding of images
Hu Yu Tian
Dept. of Inf. Eng., Chinese Univ. of Hong Kong, Shatin, Hong Kong
vol. 6, no. 1, pp. 153-62, Feb. 1998

In this paper, we present a fuzzy logic-based nonlinear predictor for predictive coding of images. We define five local structure patterns of images: uniform area, horizontal contour (0 degrees ), vertical contour (90 degrees ), 45 degrees , and 135 degrees diagonal contours. Their membership functions are derived with the gradient-based edge detection method and predicted values for different patterns are defined by linear extrapolation from available neighborhood pixel values. The predicted value of the current pixel can be obtained based on the membership functions and the defined predicted values for the different patterns. A set of parameters to characterize the proposed fuzzy predictor are determined from empirical data. Success in the use of the proposed predictor is demonstrated, by using simulation results through the reduction in the entropy as compared to those of existing linear and nonlinear ones. It is also shown that the proposed fuzzy predictor can be efficiently implemented.

Application of fuzzy logic in computer-aided VLSI design
E. Shragowitz, Yong Lee Jun, E. Q. Kang
Dept. of Comput. Sci., Minnesota Univ., Minneapolis, MN, USA
vol. 6, no. 1, pp. 163-72, Feb. 1998

Application of fuzzy logic structures in CAD of digital electronics substantially improves quality of design solutions by providing designers with flexibility in formulating goals and selecting tradeoffs. In addition, the following aspects of a design process are positively impacted by application of fuzzy logic: utilization of domain knowledge, interpretation of uncertainties in design data, and adaptation of design algorithms. We successfully applied fuzzy logic structures in conjunction with constructive and iterative algorithms for selecting of design solutions for different stages of the design process. We also introduced fuzzy logic software development tool to be used in CAD applications.

Hardware and software effective configurations for multi-input fuzzy logic controllers
S. Bolognani, M. Zigliotto
Dept. of Electr. Eng., Padova Univ., Italy
vol. 6, no. 1, pp. 173-9, Feb. 1998

This paper proposes two novel approaches to the simplification of multi-input fuzzy logic controllers (FLC). By these approaches either a hierarchical or a parallel structure is derived for a multi-input FLC, leading to the implementation of faster controllers with reduced memory demand. Both these features can be used profitably in the realization of hardware and software effective FLC for the industrial field applications. Experimental tests and comparative considerations are also included.